%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP200-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:31:47 PM UTC 2026
% Result : Unsatisfiable 16.90s 3.21s
% Output : CNFRefutation 16.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 16
% Syntax : Number of formulae : 85 ( 85 unt; 6 def)
% Number of atoms : 128 ( 84 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 7 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 99 ( 0 sgn 99 !; 0 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(X0,identity) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
fof(f3,axiom,
! [X0,X1] : multiply(X0,left_division(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_left_division) ).
fof(f4,axiom,
! [X0,X1] : left_division(X0,multiply(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_division_multiply) ).
fof(f5,axiom,
! [X0,X1] : multiply(right_division(X0,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_right_division) ).
fof(f6,axiom,
! [X0,X1] : right_division(multiply(X0,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_division_multiply) ).
fof(f7,axiom,
! [X0] : multiply(X0,right_inverse(X0)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f8,plain,
! [X0] : identity = multiply(X0,right_inverse(X0)),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X0] : multiply(left_inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f10,plain,
! [X0] : identity = multiply(left_inverse(X0),X0),
inference(reorient_equations,[],[f9]) ).
fof(f11,axiom,
! [X2,X0,X1] : multiply(multiply(X0,multiply(X1,X2)),X0) = multiply(multiply(X0,X1),multiply(X2,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',moufang1) ).
fof(f12,negated_conjecture,
multiply(multiply(multiply(a,b),c),b) != multiply(a,multiply(b,multiply(c,b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_moufang2) ).
tcf(c_59,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_60,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(cnf_transformation,[],[f2]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : multiply(X0,left_division(X0,X1)) = X1,
inference(cnf_transformation,[],[f3]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] : left_division(X0,multiply(X0,X1)) = X1,
inference(cnf_transformation,[],[f4]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] : multiply(right_division(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f5]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : right_division(multiply(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f6]) ).
tcf(c_65,plain,
! [X0: $i] : multiply(X0,right_inverse(X0)) = identity,
inference(cnf_transformation,[],[f8]) ).
tcf(c_66,plain,
! [X0: $i] : multiply(left_inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f10]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,multiply(X1,X2)),X0) = multiply(multiply(X0,X1),multiply(X2,X0)),
inference(cnf_transformation,[],[f11]) ).
tcf(c_68,negated_conjecture,
multiply(multiply(multiply(a,b),c),b) != multiply(a,multiply(b,multiply(c,b))),
inference(cnf_transformation,[],[f12]) ).
tcf(c_103,definition,
iPr_def_10 = multiply(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_104,definition,
iPr_def_11 = multiply(iPr_def_10,c),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_105,definition,
iPr_def_12 = multiply(iPr_def_11,b),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_106,definition,
iPr_def_13 = multiply(c,b),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_107,definition,
iPr_def_14 = multiply(b,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_108,definition,
iPr_def_15 = multiply(a,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_109,negated_conjecture,
iPr_def_12 != iPr_def_15,
inference(demodulation,[status(thm)],[c_68,c_106,c_107,c_108,c_103,c_104,c_105]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,multiply(X1,X2)),X0) = multiply(multiply(X0,X1),multiply(X2,X0)),
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_111,plain,
! [X0: $i] : multiply(left_inverse(X0),X0) = identity,
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_112,plain,
! [X0: $i] : multiply(X0,right_inverse(X0)) = identity,
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i] : right_division(multiply(X0,X1),X1) = X0,
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i] : multiply(right_division(X0,X1),X1) = X0,
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i] : left_division(X0,multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_62]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i] : multiply(X0,left_division(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_61]) ).
tcf(c_117,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_60]) ).
tcf(c_118,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(demodulation,[status(thm)],[c_59]) ).
tcf(c_308,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,identity),multiply(X1,X0)) = multiply(multiply(X0,X1),X0),
inference(superposition,[status(thm)],[c_118,c_110]) ).
tcf(c_327,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,X1),X0) = multiply(X0,multiply(X1,X0)),
inference(demodulation,[status(thm)],[c_308,c_117]) ).
tcf(c_632,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),multiply(X2,X0)) = multiply(X0,multiply(multiply(X1,X2),X0)),
inference(superposition,[status(thm)],[c_327,c_110]) ).
tcf(c_2093,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,multiply(X1,X2)),X0) = multiply(X0,multiply(multiply(X1,X2),X0)),
inference(demodulation,[status(thm)],[c_110,c_632]) ).
tcf(c_5406,plain,
! [X0: $i] : multiply(b,multiply(multiply(X0,iPr_def_11),b)) = multiply(multiply(b,X0),iPr_def_12),
inference(superposition,[status(thm)],[c_105,c_632]) ).
tcf(c_5454,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(multiply(X1,left_inverse(X0)),X0)) = multiply(multiply(X0,X1),identity),
inference(superposition,[status(thm)],[c_111,c_632]) ).
tcf(c_5457,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(multiply(right_inverse(X0),X1),X0)) = multiply(identity,multiply(X1,X0)),
inference(superposition,[status(thm)],[c_112,c_632]) ).
tcf(c_5515,plain,
! [X0: $i] : left_division(X0,X0) = identity,
inference(superposition,[status(thm)],[c_117,c_115]) ).
tcf(c_5517,plain,
! [X0: $i] : left_division(X0,identity) = right_inverse(X0),
inference(superposition,[status(thm)],[c_112,c_115]) ).
tcf(c_5520,plain,
left_division(a,iPr_def_10) = b,
inference(superposition,[status(thm)],[c_103,c_115]) ).
tcf(c_5521,plain,
left_division(c,iPr_def_13) = b,
inference(superposition,[status(thm)],[c_106,c_115]) ).
tcf(c_5522,plain,
left_division(iPr_def_10,iPr_def_11) = c,
inference(superposition,[status(thm)],[c_104,c_115]) ).
tcf(c_5524,plain,
left_division(b,iPr_def_14) = iPr_def_13,
inference(superposition,[status(thm)],[c_107,c_115]) ).
tcf(c_5525,plain,
left_division(a,iPr_def_15) = iPr_def_14,
inference(superposition,[status(thm)],[c_108,c_115]) ).
tcf(c_5528,plain,
! [X0: $i,X1: $i] : right_division(X0,left_division(X1,X0)) = X1,
inference(superposition,[status(thm)],[c_116,c_113]) ).
tcf(c_5537,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,X1),X0) = multiply(X0,multiply(X1,X0)),
inference(superposition,[status(thm)],[c_118,c_2093]) ).
tcf(c_5602,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(multiply(right_inverse(X0),X1),X0)) = multiply(X1,X0),
inference(demodulation,[status(thm)],[c_5457,c_118]) ).
tcf(c_5603,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(multiply(X1,left_inverse(X0)),X0)) = multiply(X0,X1),
inference(demodulation,[status(thm)],[c_5454,c_117]) ).
tcf(c_5649,plain,
! [X0: $i] : multiply(left_inverse(X0),multiply(X0,left_inverse(X0))) = multiply(identity,left_inverse(X0)),
inference(superposition,[status(thm)],[c_111,c_5537]) ).
tcf(c_5661,plain,
! [X0: $i,X1: $i] : right_division(multiply(X0,multiply(X1,X0)),X0) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_5537,c_113]) ).
tcf(c_5890,plain,
multiply(a,b) = iPr_def_10,
inference(superposition,[status(thm)],[c_5520,c_116]) ).
tcf(c_5891,plain,
multiply(c,b) = iPr_def_13,
inference(superposition,[status(thm)],[c_5521,c_116]) ).
tcf(c_5892,plain,
multiply(iPr_def_10,c) = iPr_def_11,
inference(superposition,[status(thm)],[c_5522,c_116]) ).
tcf(c_5894,plain,
multiply(b,iPr_def_13) = iPr_def_14,
inference(superposition,[status(thm)],[c_5524,c_116]) ).
tcf(c_5895,plain,
multiply(a,iPr_def_14) = iPr_def_15,
inference(superposition,[status(thm)],[c_5525,c_116]) ).
tcf(c_5968,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,left_inverse(X1)),X1) = left_division(X1,multiply(X1,X0)),
inference(superposition,[status(thm)],[c_5603,c_115]) ).
tcf(c_6076,plain,
! [X0: $i] : multiply(multiply(b,right_division(X0,iPr_def_11)),iPr_def_12) = multiply(b,multiply(X0,b)),
inference(superposition,[status(thm)],[c_114,c_5406]) ).
tcf(c_6126,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,left_inverse(X1)),X1) = X0,
inference(demodulation,[status(thm)],[c_5968,c_115]) ).
tcf(c_6127,plain,
! [X0: $i] : multiply(left_inverse(X0),multiply(X0,left_inverse(X0))) = left_inverse(X0),
inference(demodulation,[status(thm)],[c_5649,c_118]) ).
tcf(c_6715,plain,
! [X0: $i] : left_division(left_inverse(X0),left_inverse(X0)) = multiply(X0,left_inverse(X0)),
inference(superposition,[status(thm)],[c_6127,c_115]) ).
tcf(c_6983,plain,
! [X0: $i] : multiply(X0,left_inverse(X0)) = identity,
inference(demodulation,[status(thm)],[c_6715,c_5515]) ).
tcf(c_7487,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(right_inverse(X0),X1)) = right_division(multiply(X1,X0),X0),
inference(superposition,[status(thm)],[c_5602,c_5661]) ).
tcf(c_7555,plain,
! [X0: $i] : left_division(X0,identity) = left_inverse(X0),
inference(superposition,[status(thm)],[c_6983,c_115]) ).
tcf(c_7608,plain,
! [X0: $i,X1: $i] : multiply(X0,left_inverse(X1)) = right_division(X0,X1),
inference(superposition,[status(thm)],[c_6126,c_113]) ).
tcf(c_7727,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(right_inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_7487,c_113]) ).
tcf(c_8244,plain,
! [X0: $i] : right_inverse(X0) = left_inverse(X0),
inference(superposition,[status(thm)],[c_7555,c_5517]) ).
tcf(c_9432,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(left_inverse(X0),X1)) = X1,
inference(light_normalisation,[status(thm)],[c_7727,c_8244]) ).
tcf(c_9436,plain,
! [X0: $i,X1: $i] : left_division(left_inverse(X0),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_116,c_9432]) ).
tcf(c_9452,plain,
! [X0: $i,X1: $i] : multiply(left_inverse(X0),X1) = left_division(X0,X1),
inference(superposition,[status(thm)],[c_9432,c_115]) ).
tcf(c_10385,plain,
! [X0: $i,X1: $i] : right_division(X0,multiply(X1,X0)) = left_inverse(X1),
inference(superposition,[status(thm)],[c_9436,c_5528]) ).
tcf(c_11329,plain,
right_division(b,iPr_def_10) = left_inverse(a),
inference(superposition,[status(thm)],[c_5890,c_10385]) ).
tcf(c_11333,plain,
right_division(c,iPr_def_11) = left_inverse(iPr_def_10),
inference(superposition,[status(thm)],[c_5892,c_10385]) ).
tcf(c_19860,plain,
multiply(multiply(b,left_inverse(iPr_def_10)),iPr_def_12) = multiply(b,multiply(c,b)),
inference(superposition,[status(thm)],[c_11333,c_6076]) ).
tcf(c_19970,plain,
left_division(a,iPr_def_12) = iPr_def_14,
inference(demodulation,[status(thm)],[c_19860,c_5891,c_5894,c_11329,c_7608,c_9452]) ).
tcf(c_20906,plain,
multiply(a,iPr_def_14) = iPr_def_12,
inference(superposition,[status(thm)],[c_19970,c_116]) ).
tcf(c_21266,plain,
iPr_def_12 = iPr_def_15,
inference(superposition,[status(thm)],[c_20906,c_5895]) ).
tcf(c_21777,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_21266,c_109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP200-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.36 % Computer : n001.cluster.edu
% 0.03/0.36 % Model : x86_64 x86_64
% 0.03/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.36 % Memory : 8046.5625MB
% 0.03/0.36 % OS : Linux 6.8.0-71-generic
% 0.03/0.36 % CPULimit : 300
% 0.03/0.36 % WCLimit : 300
% 0.03/0.36 % DateTime : Wed Sep 23 14:12:50 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.39 Running UEQ theorem proving
% 0.03/0.39 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.40
% 0.03/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.40
% 0.03/0.40 % Detected problem language: tptp
% 0.03/0.42 % Proving...
% 16.90/3.21 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 16.90/3.21 % SZS status Started for theBenchmark.p
% 16.90/3.21 % SZS status Unsatisfiable for theBenchmark.p
% 16.90/3.21
% 16.90/3.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 16.90/3.21
% 16.90/3.21 % ------ iProver source info
% 16.90/3.21
% 16.90/3.21 % git: date: 2026-07-19 20:42:38 +0200
% 16.90/3.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 16.90/3.21 % git: non_committed_changes: false
% 16.90/3.21
% 16.90/3.21 % ------ Parsing...% successful
% 16.90/3.21
% 16.90/3.21
% 16.90/3.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 16.90/3.21
% 16.90/3.21 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 16.90/3.21
% 16.90/3.21 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 16.90/3.21
% 16.90/3.21 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 16.90/3.21 % ------ Proving...
% 16.90/3.21 % ------ Problem Properties
% 16.90/3.21
% 16.90/3.21 %
% 16.90/3.21 % clauses 16
% 16.90/3.21 % conjectures 1
% 16.90/3.21 % EPR 1
% 16.90/3.21 % Horn 16
% 16.90/3.21 % unary 16
% 16.90/3.21 % binary 0
% 16.90/3.21 % lits 16
% 16.90/3.21 % lits eq 16
% 16.90/3.21 % fd_pure 0
% 16.90/3.21 % fd_pseudo 0
% 16.90/3.21 % fd_cond 0
% 16.90/3.21 % fd_pseudo_cond 0
% 16.90/3.21 % AC symbols 0
% 16.90/3.21
% 16.90/3.21 % ------ Input Options Time Limit: Unbounded
% 16.90/3.21
% 16.90/3.21
% 16.90/3.21 % ------
% 16.90/3.21 % Current options:
% 16.90/3.21 % ------
% 16.90/3.21
% 16.90/3.21
% 16.90/3.21 %
% 16.90/3.21
% 16.90/3.21 % ------ Proving...
% 16.90/3.21 %
% 16.90/3.21
% 16.90/3.21 % SZS status Unsatisfiable for theBenchmark.p
% 16.90/3.21
% 16.90/3.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 16.90/3.21
% 16.90/3.21
%------------------------------------------------------------------------------